Critical exponents of a multicomponent anisotropic t-J model in one dimension

A recently presented anisotropic generalization of the multicomponent supersymmetric $t-J$ model in one dimension is investigated. This model of fermions with general spin-$S$ is solved by Bethe ansatz for the ground state and the low-lying excitations. Due to the anisotropy of the interaction the model possesses $2S$ massive modes and one single gapless excitation. The physical properties indicate the existence of Cooper-type multiplets of $2S+1$ fermions with finite binding energy. The critical behaviour is described by a $c=1$ conformal field theory with continuously varying exponents depending on the particle density. There are two distinct regimes of the phase diagram with dominating density-density and multiplet-multiplet correlations, respectively. The effective mass of the charge carriers is calculated. In comparison to the limit of isotropic interactions the mass is strongly enhanced in general.Comment: 10 pages, 3 Postscript figures appended as uuencoded compressed tar-file to appear in Z. Phys. B, preprint Cologne-94-474

Ground-state properties of the Rokhsar-Kivelson dimer model on the triangular lattice

We explicitly show that the Rokhsar-Kivelson dimer model on the triangular lattice is a liquid with topological order. Using the Pfaffian technique, we prove that the difference in local properties between the two topologically degenerate ground states on the cylinders and on the tori decreases exponentially with the system size. We compute the relevant correlation length and show that it equals the correlation length of the vison operator.Comment: 10 pages, 9 figure

Exclusion statistics: A resolution of the problem of negative weights

We give a formulation of the single particle occupation probabilities for a system of identical particles obeying fractional exclusion statistics of Haldane. We first derive a set of constraints using an exactly solvable model which describes an ideal exclusion statistics system and deduce the general counting rules for occupancy of states obeyed by these particles. We show that the problem of negative probabilities may be avoided with these new counting rules.Comment: REVTEX 3.0, 14 page

Alternative Technique for "Complex" Spectra Analysis

. The choice of a suitable random matrix model of a complex system is very sensitive to the nature of its complexity. The statistical spectral analysis of various complex systems requires, therefore, a thorough probing of a wide range of random matrix ensembles which is not an easy task. It is highly desirable, if possible, to identify a common mathematcal structure among all the ensembles and analyze it to gain information about the ensemble- properties. Our successful search in this direction leads to Calogero Hamiltonian, a one-dimensional quantum hamiltonian with inverse-square interaction, as the common base. This is because both, the eigenvalues of the ensembles, and, a general state of Calogero Hamiltonian, evolve in an analogous way for arbitrary initial conditions. The varying nature of the complexity is reflected in the different form of the evolution parameter in each case. A complete investigation of Calogero Hamiltonian can then help us in the spectral analysis of complex systems.Comment: 20 pages, No figures, Revised Version (Minor Changes

Test of Replica Theory: Thermodynamics of 2D Model Systems with Quenched Disorder

We study the statistics of thermodynamic quantities in two related systems with quenched disorder: A (1+1)-dimensional planar lattice of elastic lines in a random potential and the 2-dimensional random bond dimer model. The first system is examined by a replica-symmetric Bethe ansatz (RBA) while the latter is studied numerically by a polynomial algorithm which circumvents slow glassy dynamics. We establish a mapping of the two models which allows for a detailed comparison of RBA predictions and simulations. Over a wide range of disorder strength, the effective lattice stiffness and cumulants of various thermodynamic quantities in both approaches are found to agree excellently. Our comparison provides, for the first time, a detailed quantitative confirmation of the replica approach and renders the planar line lattice a unique testing ground for concepts in random systems.Comment: 16 pages, 14 figure

SU(4) Spin-Orbital Two-Leg Ladder, Square and Triangle Lattices

Based on the generalized valence bond picture, a Schwinger boson mean field theory is applied to the symmetric SU(4) spin-orbital systems. For a two-leg SU(4) ladder, the ground state is a spin-orbital liquid with a finite energy gap, in good agreement with recent numerical calculations. In two-dimensional square and triangle lattices, the SU(4) Schwinger bosons condense at (\pi/2,\pi/2) and (\pi/3,\pi/3), respectively. Spin, orbital, and coupled spin-orbital static susceptibilities become singular at the wave vectors, twice of which the bose condensation arises at. It is also demonstrated that there are spin, orbital, and coupled spin-orbital long-range orderings in the ground state.Comment: 5 page

Damage measurements on the NWTC direct-drive, Variable-Speed Test Bed

The NWTC (National Wind Technology Center) Variable-Speed Test Bed turbine is a three-bladed, 10-meter, downwind machine that can be run in either fixed-speed or variable-speed mode. In the variable-speed mode, the generator torque is regulated, using a discrete-stepped load bank to maximize the turbine`s power coefficient. At rated power, a second control loop that uses blade pitch to maintain rotor speed essentially as before, i.e., using the load bank to maintain either generator power or (optionally) generator torque. In this paper, the authors will use this turbine to study the effect of variable-speed operation on blade damage. Using time-series data obtained from blade flap and edge strain gauges, the load spectrum for the turbine is developed using rainflow counting techniques. Miner`s rule is then used to determine the damage rates for variable-speed and fixed-speed operation. The results illustrate that the controller algorithm used with this turbine introduces relatively large load cycles into the blade that significantly reduce its service lifetime, while power production is only marginally increased

Determinant Representations of Correlation Functions for the Supersymmetric t-J Model

Working in the $F$-basis provided by the factorizing $F$-matrix, the scalar products of Bethe states for the supersymmetric t-J model are represented by determinants. By means of these results, we obtain determinant representations of correlation functions for the model.Comment: Latex File, 41 pages, no figure; V2: minor typos corrected, V3: This version will appear in Commun. Math. Phy

Optical properties of the pseudogap state in underdoped cuprates

Recent optical measurements of deeply underdoped cuprates have revealed that a coherent Drude response persists well below the end of the superconducting dome. In addition, no large increase in optical effective mass has been observed, even at dopings as low as 1%. We show that this behavior is consistent with the resonating valence bond spin-liquid model proposed by Yang, Rice, and Zhang. In this model, the overall reduction in optical conductivity in the approach to the Mott insulating state is caused not by an increase in effective mass, but by a Gutzwiller factor, which describes decreased coherence due to correlations, and by a shrinking of the Fermi surface, which decreases the number of available charge carriers. We also show that in this model, the pseudogap does not modify the low-temperature, low-frequency behavior, though the magnitude of the conductivity is greatly reduced by the Gutzwiller factor. Similarly, the profile of the temperature dependence of the microwave conductivity is largely unchanged in shape, but the Gutzwiller factor is essential in understanding the observed difference in magnitude between ortho-I and -II YBa$_2$Cu$_3$O$_y$.Comment: 9 pages, 6 figures, submitted to Eur. Phys. J.

Exact diagonalization of the generalized supersymmetric t-J model with boundaries

We study the generalized supersymmetric $t-J$ model with boundaries in three different gradings: FFB, BFF and FBF. Starting from the trigonometric R-matrix, and in the framework of the graded quantum inverse scattering method (QISM), we solve the eigenvalue problems for the supersymmetric $t-J$ model. A detailed calculations are presented to obtain the eigenvalues and Bethe ansatz equations of the supersymmetric $t-J$ model with boundaries in three different backgrounds.Comment: Latex file, 32 page